Starting with polynomial:
P : 35/8*t^4 - 15/4*t^2 + 3/8
Extension levels are: 4 5 18
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Trying to find an order 5 Kronrod extension for:
P1 : 35/8*t^4 - 15/4*t^2 + 3/8
Solvable: 1
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Trying to find an order 18 Kronrod extension for:
P2 : 35/8*t^9 - 855/88*t^7 + 45297/6292*t^5 - 24885/12584*t^3 + 1845/12584*t
Solvable: 1
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Ending with final polynomial:
P : 35/8*t^27 - 17051623981426098121518663647625088809428655/585364767164693998181033410799179225938796*t^25 + 18000580010832558446771895042777371086445214015123/208765661291150796899280117694240877497264083032*t^23 - 116338009644942225880896574532192736503634158407863/778126555721562061170044075042170543398893400392*t^21 + 4260077402805391864298131540313779976368603680525867/25289113060950766988026432438870542660464035512740*t^19 - 241970246961921950827601193275519168424691008233489139/1871394366510356757113956000476420156874338627942760*t^17 + 322485432350109610159424452277009071858924440883644993/4678485916275891892784890001191050392185846569856900*t^15 - 262888332727470865420265803176201283930249543718690277/10292669015806962164126758002620310862808862453685180*t^13 + 317989204387031156516166321001075956931796153881184091/49088113767694742628912230474035328730319190163729320*t^11 - 475510678394976006847180747876504253953884129137331/437209858496052683119918514664319574072253229345255*t^9 + 14755161481203080628380211544631944400092238650904703/129414118114831594203495880340638593925386955886195480*t^7 - 21835786202536199470279622914542139535067810868212009/3235352952870789855087397008515964848134673897154887000*t^5 + 15116401092486036731341121958471485158851832972629/80883823821769746377184925212899121203366847428872175*t^3 - 269285006023900657557916585857041156167659921939/173604304788188723931518863871588357704787379847335400*t
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Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 current precision for weights: 53
Linear system for weights solvable: 0
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 1
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
Sufficient bits for target precision reached
-------------------------------------------------
The nodes are:
| (0.99547212473580896734 + 6.0201238127091121677e-448j)  +/-  (2.36e-119, 2.36e-119j)
| (0.23092596341761495096 - 2.2449240649321333156e-452j)  +/-  (1.83e-125, 1.83e-125j)
| (-0.90553078178743610168 - 5.4490517770515637447e-448j)  +/-  (8.25e-119, 8.25e-119j)
| (0.54507721421704155381 + 4.0831014950485070986e-460j)  +/-  (3.9e-122, 3.9e-122j)
| (0.94474904356228761431 - 2.6404033991268575995e-456j)  +/-  (9.45e-119, 9.45e-119j)
| (0.97656025073757311153 + 4.7999682189142366585e-458j)  +/-  (6.29e-119, 6.29e-119j)
| (-0.44451270834739557553 + 4.7471916246296588231e-462j)  +/-  (3.88e-123, 3.88e-123j)
| (-0.94474904356228761431 - 6.5246400520211636274e-462j)  +/-  (8.6e-119, 8.6e-119j)
| (-0.99547212473580896734 - 6.6468621234802370046e-473j)  +/-  (2.11e-119, 2.11e-119j)
| (4.8070365374667322508e-494 - 5.1012660895716499665e-494j)  +/-  (1.89e-492, 1.89e-492j)
| (0.90553078178743610168 - 1.9667133933759870295e-484j)  +/-  (8.45e-119, 8.45e-119j)
| (-0.97656025073757311153 - 7.1456280965978259864e-486j)  +/-  (6.56e-119, 6.56e-119j)
| (-0.86113631159405257522 + 1.5214330846877932729e-493j)  +/-  (4.61e-119, 4.61e-119j)
| (-0.80216046975514600414 - 1.0126176459519799179e-498j)  +/-  (1.31e-119, 1.31e-119j)
| (0.11702146111588388992 + 4.1078506266053961882e-507j)  +/-  (7.93e-127, 7.93e-127j)
| (0.86113631159405257522 + 9.5622855627468277767e-499j)  +/-  (4.42e-119, 4.42e-119j)
| (0.44451270834739557553 - 1.5666228434811700507e-504j)  +/-  (3.83e-123, 3.83e-123j)
| (0.6402862174963099824 - 3.112550508314490597e-503j)  +/-  (3.51e-121, 3.51e-121j)
| (-0.72718762954385476729 + 1.7181384035002061614e-502j)  +/-  (2.41e-120, 2.41e-120j)
| (-0.3399810435848562648 + 1.1772142172114080379e-506j)  +/-  (3.4e-124, 3.4e-124j)
| (0.3399810435848562648 - 3.0153128137499546075e-507j)  +/-  (3.13e-124, 3.13e-124j)
| (0.80216046975514600414 + 4.4669414878046282826e-503j)  +/-  (1.23e-119, 1.23e-119j)
| (-0.11702146111588388992 - 1.4555531218276001413e-510j)  +/-  (7.93e-127, 7.93e-127j)
| (-0.6402862174963099824 + 6.3838266190089329445e-506j)  +/-  (3.5e-121, 3.5e-121j)
| (-0.54507721421704155381 - 2.6876697950930600755e-510j)  +/-  (3.96e-122, 3.96e-122j)
| (-0.23092596341761495096 - 6.8151965920572194976e-515j)  +/-  (1.83e-125, 1.83e-125j)
| (0.72718762954385476729 - 6.1847359742259950161e-517j)  +/-  (2.25e-120, 2.25e-120j)
-------------------------------------------------
The weights are:
| (0.011576293210418411597 - 8.3588491470772131399e-448j)  +/-  (3.72e-35, 2.96e-92j)
| (0.11158582935504836175 + 3.004333034159262348e-448j)  +/-  (1.12e-35, 8.91e-93j)
| (0.040864933490843992437 - 1.5134746755321011098e-448j)  +/-  (2.95e-36, 2.35e-93j)
| (0.098293270247317156445 - 4.439712116750048834e-448j)  +/-  (8.56e-36, 6.81e-93j)
| (0.036733583437048252841 - 1.4332661966977004829e-447j)  +/-  (5.42e-36, 4.31e-93j)
| (0.025939895432915034211 + 1.5117754344758743498e-447j)  +/-  (7.47e-36, 5.95e-93j)
| (0.10258810213754148795 + 8.2075901870855540808e-449j)  +/-  (6.59e-37, 5.24e-94j)
| (0.036733583437048252841 - 3.341832384578055459e-448j)  +/-  (6.24e-37, 4.97e-94j)
| (0.011576293210418411597 - 1.58418970073678278e-449j)  +/-  (6.25e-38, 4.97e-95j)
| (0.1175853042816209324 + 2.0819323873203311801e-448j)  +/-  (6.25e-38, 4.97e-95j)
| (0.040864933490843992437 + 1.5420981637752743978e-447j)  +/-  (8.85e-38, 7.04e-95j)
| (0.025939895432915034211 + 7.8735485465559222883e-449j)  +/-  (1.07e-37, 8.55e-95j)
| (0.050270002354485501179 + 5.5714834107880210051e-448j)  +/-  (2.6e-38, 2.07e-95j)
| (0.067617960140870657706 - 1.8068814666246259108e-448j)  +/-  (5.93e-39, 4.72e-96j)
| (0.11591483684071257408 - 2.4930912913983242174e-448j)  +/-  (3.51e-39, 2.79e-96j)
| (0.050270002354485501179 - 1.3437276493555305278e-447j)  +/-  (1.04e-39, 8.24e-97j)
| (0.10258810213754148795 + 3.9911403957220204065e-448j)  +/-  (4.86e-40, 3.87e-97j)
| (0.091613831669258561063 + 5.1382096615166679209e-448j)  +/-  (1.69e-40, 1.34e-97j)
| (0.08159287827334530469 + 5.6222826670647398768e-449j)  +/-  (8.59e-41, 6.87e-98j)
| (0.10661593126938423786 - 1.1811709746312553747e-448j)  +/-  (2.51e-41, 2e-98j)
| (0.10661593126938423786 - 3.5334428817807075695e-448j)  +/-  (1.64e-40, 1.3e-97j)
| (0.067617960140870657706 + 9.3226079482336924134e-448j)  +/-  (1.61e-41, 1.27e-98j)
| (0.11591483684071257408 - 1.7680731107521722984e-448j)  +/-  (1.91e-41, 1.53e-98j)
| (0.091613831669258561063 + 2.0573552541209377752e-450j)  +/-  (4.41e-42, 3.51e-99j)
| (0.098293270247317156445 - 4.3599868552201562339e-449j)  +/-  (3.39e-42, 2.7e-99j)
| (0.11158582935504836175 + 1.4903537676362186095e-448j)  +/-  (3.04e-42, 2.47e-99j)
| (0.08159287827334530469 - 6.5288281152470244404e-448j)  +/-  (1.25e-42, 8.51e-100j)
